FANON

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Canon

The two never interacted on-screen in canon. However, they share two events together in Danganronpa V3's bonus mode, Ultimate Talent Development Plan.

In one event, Mikan is chasing after Mondo (because his hand was bleeding everywhere, which he didn't notice), only she keeps tripping and falling and apologises repeatedly. Mondo yells at her to calm down, leading Mikan to start crying and pleading with him not to hit her. Mondo, of course, says he'd never do anything so pathetic and apologises for shouting and promises he's not mad at her. When Mikan calms down and asks him to come to the infirmary so she can treat his injury, Mondo says getting his hands all scraped up from fights is no big deal to him, but he agrees anyway so Mikan won't cry anymore.

In the other event, Mikan checks up on Mondo to see if he injured himself again. Mondo is at first annoyed that Mikan views him as the type to injure himself often, but upon seeing her afraid of him, he assures her that he's not mad at her for thinking so and promises that he'll control his rage.

Mikan – “I'll try not to cry or apologize too much in front of you, so...please forgive me...”

Mondo – “Right. Good luck.”

— Mondo promises to control his rage while Mikan promises to cry and apologize less around him.

Fanon

Monkan is one of several ships that sailed as a result of the interactions between characters in Danganronpa V3's bonus mode, Ultimate Talent Development Plan. It gained its popularity because of the two's "Nice Girl, Bad Boy" status, as well as due to their personalities being considered matching, with Mondo's talent causing him to get injured often and Mikan treating his injuries, and Mondo's showing the nice side of his personality (i.e. his code to never hit a girl) around her.

Nonetheless, because they only interact with each other in a bonus mode, only a small part of the fanbase is aware of the ship. Additionally, both characters have their much more popular ships from the canon.